The technique is using the cardioid mic pointed at the source, which gives you a mono source sent to both speakers. This is the main signal.

The side signal is a bidirectional (figure of 8) mic pointed at 90 degrees from the subject you're aiming at and so this records the ambient signal (or signal from the Side).

The mid mic is played back mono.

The side mic is duplicated, switched in polarity on one of the channels. They are panned left and right respectively.

When you point your mic directly at the source, the null spot of the figure-8 mic is pointed directly at it as well so all you get is mono "in the center" signal.

When the source moves a bit to your left, it comes in also to the left lobe of the figure-8 pickup pattern, and so that shows up via the matrix on the left side, thus creating a stereo image.

It's basically that anything on your left enters into the figure-8 with positive polarity, thus being reinforced in the left speaker and cancelled out in the right speaker. When the source is on the right, the figure-8 mic is now negative in polarity, and thus the flipped phase channel is being reinforced in the right speaker and cancelled out in the left speaker because the left speaker is now negative and canceling with the mid mic and the right side (which is flipped to positive now) is being reinforced. I think if you drew a sketch or saw a picture of it at one of the sites the other guys sent a link to would work.

There is a lot more detail to go into, having to do with phase, polarity of mics, etc. but that's the basics of what you need to know.

just a point of technical clarification, the phase cancellation does not occur in the speaker; it happens in the signal.
–
Shaun FarleyFeb 7 '11 at 23:15

@Shaun I like to think of it as sort of both. Sort of like a speaker's cone won't move if you're telling it to go forward and backwards at the same time. But you're right, that's what I meant when I wrote that - that the signal is being cancelled in the right channel and reinforced in the left channel, etc. etc.
–
UtopiaFeb 8 '11 at 0:40

in short: the side information is hidden in the figure of eight's phase information. figuratively: if a signal comes from left, it is added in phase to the mid signal: L = M + S, while it is subtracted from the right channel (R = M + (-S) -> cancellation) because of the inverted phase. if it comes from right, the opposite is the case.